Simulating the Kinetics and Thermodynamics of Transitions via Forward Flux/Umbrella Sampling

First, a technique is introduced for computing equilibrium probability distributions for transitional rare-event simulations by combining the ensemble of trajectories generated by forward flux sampling (FFS) and by umbrella sampling (US) in multiple windows along an order parameter of interest; this method is denoted FFS-US. Second, the FFS algorithm is extended to obtain rate constants of partial transitions involving intermediate states from a single simulation; this is denoted "multiple state" FFS. For the FFS-US method, a FFS algorithm (preoptimized for order parameter and staging) is used to take advantage of its zero potential bias of phase-space sampling to gather histogram data with which to jump start the US and get the equilibrium distributions. In this way, kinetic data (like the rate constants and the transition path ensemble) and the underlying free-energy landscape (or probability distribution) of the system are obtained efficiently and concurrently. The applicability of these techniques is illustrated by studying several test systems, including two that involve potential energy surfaces having multiple metastable states and transition pathways, representative of complex kinetic behavior.